


from __future__ import annotations
def      UpperCAmelCase__		(UpperCamelCase_				,UpperCamelCase_				,UpperCamelCase_				,UpperCamelCase_				,UpperCamelCase_				,):



     """simple docstring"""






     snake_case											=							len(UpperCamelCase_							)

     # If row is equal to the size of the board it means there are a queen in each row in
     # the current board (possible_board)
     if row == n:
          # We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
          # this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
          boards.append(['''. ''' * i + '''Q ''' + '''. ''' * (n - 1 - i) for i in possible_board]							)
          return

     # We iterate each column in the row to find all possible results in each row
     for col in range(UpperCamelCase_							):
          # We apply that we learned previously. First we check that in the current board
          # (possible_board) there are not other same value because if there is it means
          # that there are a collision in vertical. Then we apply the two formulas we
          # learned before:
          #
          # 45º: y - x = b or 45: row - col = b
          # 135º: y + x = b or row + col = b.
          #
          # And we verify if the results of this two formulas not exist in their variables
          # respectively.  (diagonal_right_collisions, diagonal_left_collisions)
          #
          # If any or these are True it means there is a collision so we continue to the
          # next value in the for loop.
          if (
              col in possible_board
              or row - col in diagonal_right_collisions
              or row + col in diagonal_left_collisions
          ):
               continue

          # If it is False we call dfs function again and we update the inputs
          depth_first_search(
              [*possible_board, col]				,[*diagonal_right_collisions, row - col]				,[*diagonal_left_collisions, row + col]				,UpperCamelCase_				,UpperCamelCase_				,)
def      UpperCAmelCase__		(UpperCamelCase_							):



     """simple docstring"""






     snake_case											=							[]
     depth_first_search([]				,[]				,[]				,UpperCamelCase_				,UpperCamelCase_							)

     # Print all the boards
     for board in boards:
          for column in board:
               print(UpperCamelCase_							)
          print(''''''							)

     print(len(UpperCamelCase_							)				,'''solutions were found.'''							)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 n_queens_solution(4)








from ..utils import DummyObject, requires_backends

class     A__   (       metaclass=snake_case__      ):







    """simple docstring"""

    __magic_name__         =						['flax', 'transformers']
    def __init__(			self     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(self     ,   ['''flax''', '''transformers''']       )
    @classmethod
    def 						a_     (			cls     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(cls     ,   ['''flax''', '''transformers''']       )




    @classmethod
    def 						a_     (			cls     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(cls     ,   ['''flax''', '''transformers''']       )






class     A__   (       metaclass=snake_case__      ):







    """simple docstring"""

    __magic_name__         =						['flax', 'transformers']
    def __init__(			self     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(self     ,   ['''flax''', '''transformers''']       )
    @classmethod
    def 						a_     (			cls     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(cls     ,   ['''flax''', '''transformers''']       )




    @classmethod
    def 						a_     (			cls     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(cls     ,   ['''flax''', '''transformers''']       )






class     A__   (       metaclass=snake_case__      ):







    """simple docstring"""

    __magic_name__         =						['flax', 'transformers']
    def __init__(			self     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(self     ,   ['''flax''', '''transformers''']       )
    @classmethod
    def 						a_     (			cls     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(cls     ,   ['''flax''', '''transformers''']       )




    @classmethod
    def 						a_     (			cls     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(cls     ,   ['''flax''', '''transformers''']       )






class     A__   (       metaclass=snake_case__      ):







    """simple docstring"""

    __magic_name__         =						['flax', 'transformers']
    def __init__(			self     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(self     ,   ['''flax''', '''transformers''']       )
    @classmethod
    def 						a_     (			cls     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(cls     ,   ['''flax''', '''transformers''']       )




    @classmethod
    def 						a_     (			cls     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(cls     ,   ['''flax''', '''transformers''']       )




